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  • Writer's pictureEfthimios Sifounios

How to make a pythagoras cup

Updated: Jan 28, 2023

A Pythagorean cup, also known as a "Pythagorean mug" or "drinking vessel," is a cup that features a small hole in the bottom, which is said to have been invented by the ancient Greek philosopher Pythagoras. To make a Pythagorean cup, you will need:


  • A ceramic or glass cup

  • A drill with a small drill bit (around 1/8 inch)

  • A steady hand


Instructions:


  1. Start by cleaning the cup thoroughly with soap and water.

  2. Use a pencil to mark the center of the bottom of the cup.

  3. Using the drill, carefully make a hole in the bottom of the cup, following the mark you made in step 2.

  4. Once the hole is drilled, smooth any rough edges around the hole with a file or sandpaper.

  5. Clean the cup once again with soap and water to remove any dust or debris.

  6. Your Pythagorean cup is now complete and ready to use!




Note: The cup is designed to spill liquid that is poured into it, so it is not a functional drinking vessel. It was used as a tool for teaching the Pythagorean theorem and other mathematical principles in ancient Greece.





The Pythagorean cup is a geometric demonstration of the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longer side (the hypotenuse). The cup is designed in such a way that the hole in the bottom is placed at the exact point where the two legs of a right triangle would meet if the cup were to be divided into two right triangles. When the cup is filled with liquid, it appears to be a normal cup. However, if the cup is filled past a certain level, the liquid will begin to pour out of the hole in the bottom, demonstrating the principle of the Pythagorean theorem. The amount of liquid that can be held in the cup without spilling is directly proportional to the square of the length of the cup's hypotenuse. The cup was not just a tool for teaching math, but also a symbol of Pythagorean philosophy, which emphasized self-control and moderation. The cup's design serves as a reminder that one should not overindulge in anything, whether it be food, drink, or even knowledge. It's worth noting that there is some debate over whether Pythagoras himself actually invented the cup, or if it was created by his followers to serve as a symbolic representation of his philosophy and teachings. Nevertheless, it is an interesting and unique way to demonstrate the Pythagorean theorem and its principles.



The Cup of Justice, also known as the "Pythagorean cup" or "Pythagorean mug," is a cup that features a small hole in the bottom, which is said to have been invented by the ancient Greek philosopher Pythagoras. The cup is designed in such a way that the hole in the bottom is placed at the exact point where the two legs of a right triangle would meet if the cup were to be divided into two right triangles. The Cup of Justice is not a functional drinking vessel. Instead, it is a tool for teaching the Pythagorean theorem and other mathematical principles in ancient Greece. The cup is also a symbol of Pythagorean philosophy, which emphasized self-control and moderation. The cup's design serves as a reminder that one should not overindulge in anything, whether it be food, drink, or even knowledge. When the cup is filled with liquid, it appears to be a normal cup. However, if the cup is filled past a certain level, the liquid will begin to pour out of the hole in the bottom, demonstrating the principle of the Pythagorean theorem. The amount of liquid that can be held in the cup without spilling is directly proportional to the square of the length of the cup's hypotenuse. This means that the larger the cup, the more liquid it can hold without spilling. This is symbolic of the idea that those who possess more knowledge and wisdom should be able to handle more challenges and responsibilities without becoming overwhelmed. It's worth noting that there is some debate over whether Pythagoras himself actually invented the cup, or if it was created by his followers to serve as a symbolic representation of his philosophy and teachings. Nevertheless, it is an interesting and unique way to demonstrate the Pythagorean theorem and its principles.

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